Self-Driving Car Engineer Nanodegree(Term 1)¶
Advanced Lane Findings (Udacity CarND Project 4)¶
The goals / steps of this project are the following:¶
- Compute the camera calibration matrix and distortion coefficients given a set of chessboard images.
- Apply a distortion correction to raw images.
- Use color transforms, gradients, etc., to create a thresholded binary image.
- Apply a perspective transform to rectify binary image ("birds-eye view").
- Detect lane pixels and fit to find the lane boundary.
- Determine the curvature of the lane and vehicle position with respect to center.
- Warp the detected lane boundaries back onto the original image.
- Output visual display of the lane boundaries and numerical estimation of lane curvature and vehicle position.
import numpy as np import cv2 import matplotlib.pyplot as plt import matplotlib.image as mpimg import glob,os %matplotlib inline
In [1]:
import matplotlib.pyplot as plt
import numpy as np
import cv2
import glob
%matplotlib inline
nx = 9 # the number of inside corners in x
ny = 6 # the number of inside corners in y
# Arrays to store object points and image points from all the images.
objpoints = [] # 3d points in real world space
imgpoints =[] # 2d points in image plane.
# prepare object points
objp = np.zeros((nx * ny,3),np.float32)
objp[:,:2] = np.mgrid[0:nx, 0:ny].T.reshape(-1,2)
# Make a list of calibration images
images = glob.glob('camera_cal/calibration*.jpg')
count = 0
plt.figure(figsize=(12, 8))
for fname in images:
img = cv2.imread(fname)
# Convert to grayscale
gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
# Find the chessboard corners
ret, corners = cv2.findChessboardCorners(gray, (nx, ny), None)
# If found, draw corners
# If found, add object points, image points
if ret == True:
objpoints.append(objp)
imgpoints.append(corners)
# Draw and display the corners
img_cor = cv2.drawChessboardCorners(img, (nx,ny), corners, ret)
plt.subplot(4, 5, count+1)
plt.axis('off')
plt.title(fname.split('/')[-1])
plt.imshow(img_cor)
write_name = './corners_found/corners'+ fname.split('/')[-1] +'.jpg'
cv2.imwrite(write_name, img)
count += 1
Undistort the image¶
We get all of the object points and image points, so we will use them to calibrate our camera.
In [2]:
import pickle
# Test undistortion on an image
img = cv2.imread('./camera_cal/calibration01.jpg')
img_size = (img.shape[1], img.shape[0])
# Do camera calibration given object points and image points
ret, mtx, dist, rvecs, tvecs = cv2.calibrateCamera(objpoints, imgpoints, img_size,None,None)
dst = cv2.undistort(img, mtx, dist, None, mtx)
cv2.imwrite('./output_images/calibration1_undist.jpg',dst)
# Save the camera calibration result for later use (we won't worry about rvecs / tvecs)
dist_pickle = {}
dist_pickle["mtx"] = mtx
dist_pickle["dist"] = dist
pickle.dump( dist_pickle, open( "./output_images/camera_mtx_dist.p", "wb" ) )
#dst = cv2.cvtColor(dst, cv2.COLOR_BGR2RGB)
# Visualize undistortion
f, (ax1, ax2) = plt.subplots(1, 2, figsize=(20,10))
ax1.imshow(img)
ax1.set_title('Original Image', fontsize=30)
ax2.imshow(dst)
ax2.set_title('Undistorted Image', fontsize=30)
Out[2]:
We finish the camera calibration.
2. Apply a Distortion Correction¶
In [3]:
def undistort(img):
mtx = dist_pickle['mtx']
dist = dist_pickle['dist']
return cv2.undistort(img, mtx, dist, None, mtx)
In [4]:
images = glob.glob('test_images/test*.jpg')
for img in images:
img1 = cv2.imread(img)
undist = undistort(img1)
f, (ax1, ax2) = plt.subplots(1, 2, figsize=(9,6))
ax1.imshow(cv2.cvtColor(undist, cv2.COLOR_BGR2RGB))
ax1.set_title('Original Image', fontsize=10)
ax2.imshow(cv2.cvtColor(undist, cv2.COLOR_BGR2RGB))
ax2.set_title('Undistorted Image', fontsize=10)
plt.savefig('output_images/undistorted.png'.format(None), bbox_inches="tight")
3. Create a thresholded binary image¶
We want to detect the lanes on the roads, but don't want to detect the trees or other vehicles in this prject. Fortunately, lane lines color is always white/yellow and high contrast between roads and lanes.
In this section, we apply some threshold to pick only yellow and white elements.
Applying sobel operator¶
In [5]:
def sobel_x(img, threshold_MIN=20, threshold_MAX=255):
gray = cv2.cvtColor(img, cv2.COLOR_RGB2GRAY)
sobel = cv2.Sobel(gray, cv2.CV_64F, 1, 0)
abs_sobel = np.absolute(sobel)
scaled_sobel = np.uint8(255*abs_sobel/np.max(abs_sobel))
binary_output = np.zeros_like(scaled_sobel)
binary_output[(scaled_sobel >= threshold_MIN) & (scaled_sobel <= threshold_MAX)] = 1
return binary_output
In [6]:
images = glob.glob('test_images/test*.jpg')
for img in images:
img1 = cv2.imread(img)
sobelx = sobel_x(img1)
f, (ax1, ax2) = plt.subplots(1, 2, figsize=(9,6))
ax1.imshow(cv2.cvtColor(img1, cv2.COLOR_BGR2RGB))
ax1.set_title('Original Image', fontsize=10)
ax2.imshow(sobelx, cmap='gray')
ax2.set_title('sobel_x Image', fontsize=10)
plt.savefig('output_images/sobel_x.png'.format(None), bbox_inches="tight")
In [7]:
def sobel_y(img, threshold_MIN=35, threshold_MAX=255):
gray = cv2.cvtColor(img, cv2.COLOR_RGB2GRAY)
sobel = cv2.Sobel(gray, cv2.CV_64F, 0, 1)
abs_sobel = np.absolute(sobel)
scaled_sobel = np.uint8(255*abs_sobel/np.max(abs_sobel))
binary_output = np.zeros_like(scaled_sobel)
binary_output[(scaled_sobel >= threshold_MIN) & (scaled_sobel <= threshold_MAX)] = 1
return binary_output
In [8]:
images = glob.glob('test_images/test*.jpg')
for img in images:
img1 = cv2.imread(img)
sobely = sobel_y(img1)
f, (ax1, ax2) = plt.subplots(1, 2, figsize=(9,6))
ax1.imshow(cv2.cvtColor(img1, cv2.COLOR_BGR2RGB))
ax1.set_title('Original Image', fontsize=10)
ax2.imshow(sobely, cmap='gray')
ax2.set_title('sobel_y Image', fontsize=10)
plt.savefig('output_images/sobel_y.png'.format(None), bbox_inches="tight")
Magnitude of the gradient¶
In [9]:
def gradient_magnitude(img, sobel_kernel=9, mag_threshold=(50, 255)):
gray = cv2.cvtColor(img, cv2.COLOR_RGB2GRAY)
sobel_x = cv2.Sobel(gray, cv2.CV_64F, 1, 0, ksize=sobel_kernel)
sobel_y = cv2.Sobel(gray, cv2.CV_64F, 0, 1, ksize=sobel_kernel)
gradmag = np.sqrt(sobel_x**2 + sobel_y**2)
gradmag = np.uint8(255*gradmag/np.max(gradmag))
binary_output = np.zeros_like(gradmag)
binary_output[(gradmag >= mag_threshold[0]) & (gradmag <= mag_threshold[1])] = 1
return binary_output
In [10]:
images = glob.glob('test_images/test*.jpg')
for img in images:
img1 = cv2.imread(img)
gradient_m = gradient_magnitude(img1)
f, (ax1, ax2) = plt.subplots(1, 2, figsize=(9,6))
ax1.imshow(cv2.cvtColor(img1, cv2.COLOR_BGR2RGB))
ax1.set_title('Original Image', fontsize=10)
ax2.imshow(gradient_m, cmap='gray')
ax2.set_title('gradient_magnitude Image', fontsize=10)
plt.savefig('output_images/gradient_magnitude.png'.format(None), bbox_inches="tight")
Direction of the gradient¶
In [11]:
def gradient_direction(img, sobel_kernel=15, thresh=(0.6, 1.3)):
gray = cv2.cvtColor(img, cv2.COLOR_RGB2GRAY)
sobel_x = cv2.Sobel(gray, cv2.CV_64F, 1, 0, ksize=sobel_kernel)
sobel_y = cv2.Sobel(gray, cv2.CV_64F, 0, 1, ksize=sobel_kernel)
abs_grad_dir = np.arctan2(np.absolute(sobel_y), np.absolute(sobel_x))
binary_output = np.zeros_like(abs_grad_dir)
binary_output[(abs_grad_dir >= thresh[0]) & (abs_grad_dir <= thresh[1])] = 1
return binary_output
In [12]:
images = glob.glob('test_images/test*.jpg')
for img in images:
img1 = cv2.imread(img)
gradient_d = gradient_direction(img1)
f, (ax1, ax2) = plt.subplots(1, 2, figsize=(9,6))
ax1.imshow(cv2.cvtColor(img1, cv2.COLOR_BGR2RGB))
ax1.set_title('Original Image', fontsize=10)
ax2.imshow(gradient_d, cmap='gray')
ax2.set_title('gradient_direction Image', fontsize=10)
plt.savefig('output_images/gradient_direction.png'.format(None), bbox_inches="tight")
Color Threshold¶
In [13]:
def color_thresholds(img, HLS_s_threshold=(90, 255), HSV_v_threshold=(120,255)):
hls = cv2.cvtColor(img, cv2.COLOR_RGB2HLS)
s_channel = hls[:,:,2]
s_binary = np.zeros_like(s_channel)
s_binary[(s_channel > HLS_s_threshold[0]) & (s_channel <= HLS_s_threshold[1])] = 1
hsv = cv2.cvtColor(img, cv2.COLOR_RGB2HSV)
v_channel = hsv[:,:,2]
v_binary = np.zeros_like(v_channel)
v_binary[(v_channel > HSV_v_threshold[0]) & (v_channel <= HSV_v_threshold[1])] = 1
binary_output = np.zeros_like(s_channel)
binary_output[(s_binary == 1) & (v_binary == 1)] = 1
return binary_output
In [14]:
images = glob.glob('test_images/test*.jpg')
for img in images:
img1 = cv2.imread(img)
color_t = color_thresholds(img1)
f, (ax1, ax2) = plt.subplots(1, 2, figsize=(9,6))
ax1.imshow(cv2.cvtColor(img1, cv2.COLOR_BGR2RGB))
ax1.set_title('Original Image', fontsize=10)
ax2.imshow(color_t, cmap='gray')
ax2.set_title('color_threshold Image', fontsize=10)
plt.savefig('output_images/color_threshold.png'.format(None), bbox_inches="tight")
Combine threshold¶
In [15]:
def combined_thresholds(img):
binary_x = sobel_x(img)
binary_y = sobel_y(img)
mag = gradient_magnitude(img)
direct = gradient_direction(img)
color = color_thresholds(img)
img = cv2.cvtColor(img, cv2.COLOR_RGB2GRAY)
binary_output = np.zeros_like(img)
binary_output[(binary_x == 1) & (binary_y == 1) & (mag == 1) | (color == 1) | (mag == 1) & (direct == 1)] = 1
return binary_output
In [16]:
images = glob.glob('test_images/test*.jpg')
for img in images:
img1 = cv2.imread(img)
img2 = undistort(img1)
combined_t = combined_thresholds(img2)
f, (ax1, ax2) = plt.subplots(1, 2, figsize=(9,6))
ax1.imshow(cv2.cvtColor(img1, cv2.COLOR_BGR2RGB))
ax1.set_title('Original Image', fontsize=10)
ax2.imshow(combined_t, cmap='gray')
ax2.set_title('combined_thresholds Image', fontsize=10)
plt.savefig('output_images/combined_thresholds.png'.format(None), bbox_inches="tight")
4. Apply a perspective transform¶
In [17]:
def birds_eye(img):
offset = 0
img_size = (img.shape[1], img.shape[0])
src = np.float32([[(img_size[0] / 2) - 60, img_size[1] / 2 + 100],
[((img_size[0] / 6) - 10), img_size[1]],
[(img_size[0] * 5 / 6) + 90, img_size[1]],
[(img_size[0] / 2 + 60), img_size[1] / 2 + 100]])
dst = np.float32([[(img_size[0] / 4), 0],
[(img_size[0] / 4), img_size[1]],
[(img_size[0] * 3 / 4), img_size[1]],
[(img_size[0] * 3 / 4), 0]])
M = cv2.getPerspectiveTransform(src, dst)
Minv = cv2.getPerspectiveTransform(dst, src)
# Warp the image using OpenCV warpPerspective()
warped = cv2.warpPerspective(img, M, img_size, flags=cv2.INTER_LINEAR)
return warped, M, Minv
In [18]:
images = glob.glob('test_images/test*.jpg')
for img in images:
img1 = cv2.imread(img)
img2 = undistort(img1)
warped, M, Minv = birds_eye(img2)
f, (ax1, ax2) = plt.subplots(1, 2, figsize=(9,6))
ax1.imshow(cv2.cvtColor(img1, cv2.COLOR_BGR2RGB))
ax1.set_title('Original Image', fontsize=10)
ax2.imshow(cv2.cvtColor(warped, cv2.COLOR_BGR2RGB))
ax2.set_title('birds eye Image', fontsize=10)
plt.savefig('output_images/birds_eye.png'.format(None), bbox_inches="tight")
Warped Binaly image
In [19]:
images = glob.glob('test_images/test*.jpg')
for image in images:
img1 = cv2.imread(image)
img2 = undistort(img1)
warped, M, Minv = birds_eye(img2)
new_img = combined_thresholds(warped)
f, (ax1, ax2) = plt.subplots(1, 2, figsize=(9,6))
ax1.imshow(cv2.cvtColor(img1, cv2.COLOR_BGR2RGB))
ax1.set_title('Original Image', fontsize=10)
ax2.imshow(new_img, cmap='gray')
ax2.set_title('Binary Image', fontsize=10)
plt.savefig('output_images/Binary.png'.format(None), bbox_inches="tight")
In [20]:
images = glob.glob('test_images/test*.jpg')
for img in images:
img1 = cv2.imread(img)
img2 = undistort(img1)
warped, M, Minv = birds_eye(img2)
new_img = combined_thresholds(warped)
histogram = np.sum(new_img[new_img.shape[0]/2:,:], axis=0)
# Visualize thresholds
f, (ax1, ax2) = plt.subplots(1, 2, figsize=(20,5))
ax1.imshow(new_img, cmap='gray')
ax1.set_title('Warped Binary Image', fontsize=10)
plt.plot(histogram)
ax2.set_title('Histogram', fontsize=10)
Implement Sliding Windows and Fit a Polynomial¶
In [21]:
def findlines(binary_warped):
histogram = np.sum(binary_warped[binary_warped.shape[0]/2:,:], axis=0)
# Create an output image to draw on and visualize the result
out_img = np.dstack((binary_warped, binary_warped, binary_warped))*255
# Find the peak of the left and right halves of the histogram
# These will be the starting point for the left and right lines
midpoint = np.int(histogram.shape[0]/2)
leftx_base = np.argmax(histogram[:midpoint])
rightx_base = np.argmax(histogram[midpoint:]) + midpoint
# Choose the number of sliding windows
nwindows = 9
# Set height of windows
window_height = np.int(binary_warped.shape[0]/nwindows)
# Identify the x and y positions of all nonzero pixels in the image
nonzero = binary_warped.nonzero()
nonzeroy = np.array(nonzero[0])
nonzerox = np.array(nonzero[1])
# Current positions to be updated for each window
leftx_current = leftx_base
rightx_current = rightx_base
# Set the width of the windows +/- margin
margin = 100
# Set minimum number of pixels found to recenter window
minpix = 50
# Create empty lists to receive left and right lane pixel indices
left_lane_inds = []
right_lane_inds = []
# Step through the windows one by one
for window in range(nwindows):
# Identify window boundaries in x and y (and right and left)
win_y_low = binary_warped.shape[0] - (window+1)*window_height
win_y_high = binary_warped.shape[0] - window*window_height
win_xleft_low = leftx_current - margin
win_xleft_high = leftx_current + margin
win_xright_low = rightx_current - margin
win_xright_high = rightx_current + margin
# Draw the windows on the visualization image
cv2.rectangle(out_img,(win_xleft_low,win_y_low),(win_xleft_high,win_y_high),(0,255,0), 2)
cv2.rectangle(out_img,(win_xright_low,win_y_low),(win_xright_high,win_y_high),(0,255,0), 2)
# Identify the nonzero pixels in x and y within the window
good_left_inds = ((nonzeroy >= win_y_low) & (nonzeroy < win_y_high) & (nonzerox >= win_xleft_low) & (nonzerox < win_xleft_high)).nonzero()[0]
good_right_inds = ((nonzeroy >= win_y_low) & (nonzeroy < win_y_high) & (nonzerox >= win_xright_low) & (nonzerox < win_xright_high)).nonzero()[0]
# Append these indices to the lists
left_lane_inds.append(good_left_inds)
right_lane_inds.append(good_right_inds)
# If you found > minpix pixels, recenter next window on their mean position
if len(good_left_inds) > minpix:
leftx_current = np.int(np.mean(nonzerox[good_left_inds]))
if len(good_right_inds) > minpix:
rightx_current = np.int(np.mean(nonzerox[good_right_inds]))
# Concatenate the arrays of indices
left_lane_inds = np.concatenate(left_lane_inds)
right_lane_inds = np.concatenate(right_lane_inds)
# Extract left and right line pixel positions
leftx = nonzerox[left_lane_inds]
lefty = nonzeroy[left_lane_inds]
rightx = nonzerox[right_lane_inds]
righty = nonzeroy[right_lane_inds]
# Fit a second order polynomial to each
left_fit = np.polyfit(lefty, leftx, 2)
right_fit = np.polyfit(righty, rightx, 2)
ploty = np.linspace(0, binary_warped.shape[0]-1, binary_warped.shape[0] )
left_fitx = left_fit[0]*ploty**2 + left_fit[1]*ploty + left_fit[2]
right_fitx = right_fit[0]*ploty**2 + right_fit[1]*ploty + right_fit[2]
out_img[nonzeroy[left_lane_inds], nonzerox[left_lane_inds]] = [255, 0, 0]
out_img[nonzeroy[right_lane_inds], nonzerox[right_lane_inds]] = [0, 0, 255]
return out_img, ploty, left_fitx, right_fitx, left_fit, right_fit, leftx, rightx, leftx_base, rightx_base
Visualization¶
In [22]:
images = glob.glob('test_images/test*.jpg')
for img in images:
img1 = cv2.imread(img)
img2 = undistort(img1)
warped, M, Minv = birds_eye(img2)
new_img = combined_thresholds(warped)
windows_img, ploty, left_fitx, right_fitx, left_fit, right_fit, leftx, rightx, leftx_base, rightx_base = findlines(new_img)
f, (ax1, ax2) = plt.subplots(1, 2, figsize=(20,10))
ax1.imshow(new_img, cmap='gray')
ax1.set_title('Binary Image', fontsize=10)
ax2.imshow(windows_img, cmap='gray')
ax2.set_title('Fitted', fontsize=10)
ax2.plot(left_fitx, ploty, color='yellow')
ax2.plot(right_fitx, ploty, color='yellow')
plt.savefig('output_images/finding_lines.png'.format(None), bbox_inches="tight")
Skip the sliding windows step once you know where the lines are¶
In [23]:
def shaded_lanes(binary_warped, left_fit, right_fit):
nonzero = binary_warped.nonzero()
nonzeroy = np.array(nonzero[0])
nonzerox = np.array(nonzero[1])
margin = 100
left_lane_inds = ((nonzerox > (left_fit[0]*(nonzeroy**2) + left_fit[1]*nonzeroy + left_fit[2] - margin)) & (nonzerox < (left_fit[0]*(nonzeroy**2) + left_fit[1]*nonzeroy + left_fit[2] + margin)))
right_lane_inds = ((nonzerox > (right_fit[0]*(nonzeroy**2) + right_fit[1]*nonzeroy + right_fit[2] - margin)) & (nonzerox < (right_fit[0]*(nonzeroy**2) + right_fit[1]*nonzeroy + right_fit[2] + margin)))
leftx = nonzerox[left_lane_inds]
lefty = nonzeroy[left_lane_inds]
rightx = nonzerox[right_lane_inds]
righty = nonzeroy[right_lane_inds]
# Fit a second order polynomial to each
left_fit = np.polyfit(lefty, leftx, 2)
right_fit = np.polyfit(righty, rightx, 2)
# Generate x and y values for plotting
ploty = np.linspace(0, binary_warped.shape[0]-1, binary_warped.shape[0] )
left_fitx = left_fit[0]*ploty**2 + left_fit[1]*ploty + left_fit[2]
right_fitx = right_fit[0]*ploty**2 + right_fit[1]*ploty + right_fit[2]
# Create an image to draw on and an image to show the selection window
out_img = np.dstack((binary_warped, binary_warped, binary_warped))*255
window_img = np.zeros_like(out_img)
# Color in left and right line pixels
out_img[nonzeroy[left_lane_inds], nonzerox[left_lane_inds]] = [255, 0, 0]
out_img[nonzeroy[right_lane_inds], nonzerox[right_lane_inds]] = [0, 0, 255]
# Generate a polygon to illustrate the search window area
# And recast the x and y points into usable format for cv2.fillPoly()
left_line_window1 = np.array([np.transpose(np.vstack([left_fitx-margin, ploty]))])
left_line_window2 = np.array([np.flipud(np.transpose(np.vstack([left_fitx+margin, ploty])))])
left_line_pts = np.hstack((left_line_window1, left_line_window2))
right_line_window1 = np.array([np.transpose(np.vstack([right_fitx-margin, ploty]))])
right_line_window2 = np.array([np.flipud(np.transpose(np.vstack([right_fitx+margin, ploty])))])
right_line_pts = np.hstack((right_line_window1, right_line_window2))
cv2.fillPoly(window_img, np.int_([left_line_pts]), (0,200, 0))
cv2.fillPoly(window_img, np.int_([right_line_pts]), (0,200, 0))
out_img = cv2.addWeighted(out_img, 1, window_img, 0.3, 0)
return out_img, ploty, left_fitx, right_fitx, left_fit, right_fit
Visualize the result¶
In [24]:
images = glob.glob('test_images/test*.jpg')
for img in images:
img1 = cv2.imread(img)
img2 = undistort(img1)
warped, M, Minv = birds_eye(img2)
new_img = combined_thresholds(warped)
windows_img, ploty, left_fitx, right_fitx, left_fit, right_fit, leftx, rightx, leftx_base, rightx_base = findlines(new_img)
shades_img, ploty, left_fitx, right_fitx, left_fit, right_fit = shaded_lanes(new_img, left_fit, right_fit)
f, (ax1, ax2) = plt.subplots(1, 2, figsize=(20,10))
ax1.imshow(new_img, cmap='gray')
ax1.set_title('Binary Image', fontsize=10)
ax2.imshow(shades_img, cmap='gray')
ax2.set_title('Fitted', fontsize=10)
ax2.plot(left_fitx, ploty, color='yellow')
ax2.plot(right_fitx, ploty, color='yellow')
plt.savefig('output_images/shaded_lanes.png'.format(None), bbox_inches="tight")
Another Line Finding Method: Sliding Window Search¶
In [25]:
def window_mask(width, height, img_ref, center,level):
output = np.zeros_like(img_ref)
output[int(img_ref.shape[0]-(level+1)*height):int(img_ref.shape[0]-level*height),max(0,int(center-width/2)):min(int(center+width/2),img_ref.shape[1])] = 1
return output
def find_window_centroids(image, window_width, window_height, margin):
window_centroids = [] # Store the (left,right) window centroid positions per level
window = np.ones(window_width) # Create our window template that we will use for convolutions
# First find the two starting positions for the left and right lane by using np.sum to get the vertical image slice
# and then np.convolve the vertical image slice with the window template
# Sum quarter bottom of image to get slice, could use a different ratio
l_sum = np.sum(image[int(3*image.shape[0]/4):,:int(image.shape[1]/2)], axis=0)
l_center = np.argmax(np.convolve(window,l_sum))-window_width/2
r_sum = np.sum(image[int(3*image.shape[0]/4):,int(image.shape[1]/2):], axis=0)
r_center = np.argmax(np.convolve(window,r_sum))-window_width/2+int(image.shape[1]/2)
# Add what we found for the first layer
window_centroids.append((l_center,r_center))
# Go through each layer looking for max pixel locations
for level in range(1,(int)(image.shape[0]/window_height)):
# convolve the window into the vertical slice of the image
image_layer = np.sum(image[int(image.shape[0]-(level+1)*window_height):int(image.shape[0]-level*window_height),:], axis=0)
conv_signal = np.convolve(window, image_layer)
# Find the best left centroid by using past left center as a reference
# Use window_width/2 as offset because convolution signal reference is at right side of window, not center of window
offset = window_width/2
l_min_index = int(max(l_center+offset-margin,0))
l_max_index = int(min(l_center+offset+margin,image.shape[1]))
l_center = np.argmax(conv_signal[l_min_index:l_max_index])+l_min_index-offset
# Find the best right centroid by using past right center as a reference
r_min_index = int(max(r_center+offset-margin,0))
r_max_index = int(min(r_center+offset+margin,image.shape[1]))
r_center = np.argmax(conv_signal[r_min_index:r_max_index])+r_min_index-offset
# Add what we found for that layer
window_centroids.append((l_center,r_center))
if len(window_centroids) > 0:
# Points used to draw all the left and right windows
l_points = np.zeros_like(image)
r_points = np.zeros_like(image)
# Go through each level and draw the windows
for level in range(0,len(window_centroids)):
# Window_mask is a function to draw window areas
l_mask = window_mask(window_width,window_height,image,window_centroids[level][0],level)
r_mask = window_mask(window_width,window_height,image,window_centroids[level][1],level)
# Add graphic points from window mask here to total pixels found
l_points[(l_points == 255) | ((l_mask == 1) ) ] = 255
r_points[(r_points == 255) | ((r_mask == 1) ) ] = 255
# Draw the results
template = np.array(r_points+l_points,np.uint8) # add both left and right window pixels together
zero_channel = np.zeros_like(template) # create a zero color channle
template = np.array(cv2.merge((zero_channel,template,zero_channel)),np.uint8) # make window pixels green
warpage = np.array(cv2.merge((image,image,image)),np.uint8) # making the original road pixels 3 color channels
output = cv2.addWeighted(warpage, 1, template, 0.5, 0.0) # overlay the orignal road image with window results
# If no window centers found, just display orginal road image
else:
output = np.array(cv2.merge((image,image,image)),np.uint8)
return window_centroids, output
In [26]:
# window settings
window_width = 50
window_height = 72 # Break image into 10 vertical layers since image height is 720
margin = 20 # How much to slide left and right for searching
images = glob.glob('test_images/test*.jpg')
for img in images:
img1 = cv2.imread(img)
img2 = undistort(img1)
warped, M, Minv = birds_eye(img2)
new_img = combined_thresholds(warped)
window_centroids, output = find_window_centroids(new_img, window_width, window_height, margin)
f, (ax1, ax2) = plt.subplots(1, 2, figsize=(20,10))
ax1.imshow(new_img, cmap='gray')
ax1.set_title('Binary Image', fontsize=10)
ax2.imshow(output, cmap='gray')
ax2.set_title('Fitted', fontsize=10)
plt.savefig('output_images/window_search.png'.format(None), bbox_inches="tight")
6. Determine the curvature of the lane and vehicle position with respect to center.¶
In [27]:
def calculateCurvature(left_fitx, right_fitx, ploty):
leftx = left_fitx
rightx = right_fitx
# Fit a second order polynomial to pixel positions in each lane line
left_fit = np.polyfit(ploty, leftx, 2)
left_fitx = left_fit[0]*ploty**2 + left_fit[1]*ploty + left_fit[2]
right_fit = np.polyfit(ploty, rightx, 2)
right_fitx = right_fit[0]*ploty**2 + right_fit[1]*ploty + right_fit[2]
y_eval = np.max(ploty)
left_curverad = ((1 + (2*left_fit[0]*y_eval + left_fit[1])**2)**1.5) / np.absolute(2*left_fit[0])
right_curverad = ((1 + (2*right_fit[0]*y_eval + right_fit[1])**2)**1.5) / np.absolute(2*right_fit[0])
# Define conversions in x and y from pixels space to meters
ym_per_pix = 30/600 # meters per pixel in y dimension
xm_per_pix = 3.7/540 # meters per pixel in x dimension
# Fit new polynomials to x,y in world space
left_fit_cr = np.polyfit(ploty*ym_per_pix, leftx*xm_per_pix, 2)
right_fit_cr = np.polyfit(ploty*ym_per_pix, rightx*xm_per_pix, 2)
# Calculate the new radii of curvature
left_curverad = ((1 + (2*left_fit_cr[0]*y_eval*ym_per_pix + left_fit_cr[1])**2)**1.5) / np.absolute(2*left_fit_cr[0])
right_curverad = ((1 + (2*right_fit_cr[0]*y_eval*ym_per_pix + right_fit_cr[1])**2)**1.5) / np.absolute(2*right_fit_cr[0])
# Now our radius of curvature is in meters
#print(left_curverad, 'm', right_curverad, 'm')
return left_curverad, right_curverad
In [28]:
for img in images:
img1 = cv2.imread(img)
img2 = undistort(img1)
warped, M, Minv = birds_eye(img2)
new_img = combined_thresholds(warped)
windows_img, ploty, left_fitx, right_fitx, left_fit, right_fit, leftx, rightx, leftx_base, rightx_base = findlines(new_img)
shades_img, ploty, left_fitx, right_fitx, left_fit, right_fit = shaded_lanes(new_img, left_fit, right_fit)
left_curverad, right_curverad = calculateCurvature(left_fitx, right_fitx, ploty)
f, (ax1, ax2) = plt.subplots(1, 2, figsize=(20,10))
ax1.imshow(new_img, cmap='gray')
ax1.set_title('Binary Image', fontsize=20)
ax2.imshow(shades_img, cmap='gray')
ax2.set_title('Left Radius: ' + str(left_curverad) + 'm ' + 'Right Radius: ' + str(right_curverad) + 'm', fontsize=15)
ax2.plot(left_fitx, ploty, color='yellow')
ax2.plot(right_fitx, ploty, color='yellow')
plt.savefig('output_images/curvature.png'.format(None), bbox_inches="tight")
In [29]:
def draw_lines(original, warped, Minv, ploty, left_fitx, right_fitx):
warp_zero = np.zeros_like(warped[:,:,1]).astype(np.uint8)
color_warp = np.dstack((warp_zero, warp_zero, warp_zero))
pts_left = np.array([np.transpose(np.vstack([left_fitx, ploty]))])
pts_right = np.array([np.flipud(np.transpose(np.vstack([right_fitx, ploty])))])
pts = np.hstack((pts_left, pts_right))
cv2.fillPoly(color_warp, np.int_([pts]), (0,255,0))
newwarp = cv2.warpPerspective(color_warp, Minv, (color_warp.shape[1], color_warp.shape[0]))
out_img = cv2.addWeighted(original, 1, newwarp, 0.3, 0)
return out_img
In [30]:
images = glob.glob('test_images/test*.jpg')
for img in images:
img1 = cv2.imread(img)
img2 = undistort(img1)
warped, M, Minv = birds_eye(img2)
new_img = combined_thresholds(warped)
windows_img, ploty, left_fitx, right_fitx, left_fit, right_fit, leftx, rightx, leftx_base, rightx_base = findlines(new_img)
#shades_img, ploty, left_fitx, right_fitx, left_fit, right_fit = shaded_lanes(new_img, left_fit, right_fit)
result = draw_lines(img1, warped, Minv, ploty, left_fitx, right_fitx)
f, (ax1, ax2) = plt.subplots(1, 2, figsize=(20,10))
ax1.imshow(cv2.cvtColor(img1, cv2.COLOR_BGR2RGB))
ax1.set_title('Original Image', fontsize=10)
ax2.imshow(cv2.cvtColor(result, cv2.COLOR_BGR2RGB))
ax2.set_title('result', fontsize=10)
plt.savefig('output_images/draw_lines.png'.format(None), bbox_inches="tight")
In [31]:
def process_image(input_image):
global left_fit, right_fit, ploty, left_fitx, right_fitx, index
img = undistort(input_image)
warped, M, Minv = birds_eye(img)
new_img = combined_thresholds(warped)
#Use sliding windows every 10 frames
if index == 0:
windows_img, ploty, left_fitx, right_fitx, left_fit, right_fit, leftx, rightx, leftx_base, rightx_base = findlines(new_img)
index += 1
else:
shades_img, ploty, left_fitx, right_fitx, left_fit, right_fit = shaded_lanes(new_img, left_fit, right_fit)
if index == 10:
index = 0
result = draw_lines(input_image, warped, Minv, ploty, left_fitx, right_fitx)
#Every 10 frames print out the line curverage
if index == 1:
left_curverad, right_curverad = calculateCurvature(left_fitx, right_fitx, ploty)
cv2.putText(result, "Left curverad {0:.2f}m".format(left_curverad), (10,30), cv2.FONT_HERSHEY_SIMPLEX, 1, (255,255,255),2)
cv2.putText(result, "Right curverad {0:.2f}m".format(right_curverad), (10,70), cv2.FONT_HERSHEY_SIMPLEX, 1, (255,255,255),2)
#cv2.putText(result, "Position of the car relative to the center of the lane {0:.2f}cm".format(car_position), (10,110), cv2.FONT_HERSHEY_SIMPLEX, 1, (255,255,255),2)
return result
In [32]:
from moviepy.editor import VideoFileClip
from IPython.display import HTML
index = 0
project_output = 'project_output.mp4'
clip2 = VideoFileClip('project_video.mp4')
project_clip = clip2.fl_image(process_image)
%time project_clip.write_videofile(project_output, audio=False)
In [ ]: